Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners

DOI10.1007/BF01411846zbMath0425.65054MaRDI QIDQ1135625

H. Gietl, Christoph Zenger

Publication date: 1978

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132553

zbMATH Keywords

error boundsorder of convergencepolygonal domainstandard 5-point difference scheme

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (3)

Extrapolation techniques for reducing the pollution effect of reentrant corners in the finite element method ⋮ Energy corrected FEM for optimal Dirichlet boundary control problems ⋮ Singularities and treatments of elliptic boundary value problems.

Cites Work

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• Elliptische Differenzenoperatoren unter Dirichlet-Randbedingungen
• Asymptotic expansions of the discretization error of boundary value problems of the Laplace equation in rectangular domains
• A finite element scheme for domains with corners
• Vergleich zwischen Diskretisierungsverfahren und parametrischen Methoden an einfachen Testbeispielen
• Discrete Analogues of the Dirichlet Problem with Isolated Singularities
• On the Degree of Convergence of Solutions of Difference Equations to the Solution of the Dirichlet Problem

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